Presentation

Hello! My name is David Ayotte and I’m a Ph. D. Student in Mathematics at Concordia University in Montreal. My area of research is Number Theory, more precisely I study modular forms which are mathematical objects with profond connection with numbers. For example, modular forms played a very important role in the proof of Fermat’s last theorem, a theorem that was stated by Pierre de Fermat around 1637 but was only completely proved in 1994.

For my Ph. D. thesis, I am interested in the study of the computational aspects of Drinfeld modular forms. This type of modular forms can be viewed as an analogues of the classical modular forms (the theory over \(\mathbb{C}\)) but for function fields of the forms \(\mathbb{F}_q(T)\) where \(q\) is a power of a prime number.

During the summer 2021, I participated in the program Google Summer of Code where I worked for this exciting open source organization called SageMath. SageMath is a mathematical software built on top of multiple already existing open-source computing software (such as NumPy, SciPi, matplotlib, etc). The goal of my project was to implement the graded ring of quasimodular forms into the software. I blogged about my journey here on my website (see the section GSoC).